# Solve inequality involving modulus

1. Oct 25, 2012

### utkarshakash

1. The problem statement, all variables and given/known data
Find the solution set of $\large \frac{|x-1|(x-3)(x-5)^{2010}}{(|x|-3)(|x|+1)} \geq 0$

2. Relevant equations
I am required to solve this using Wavy-Curve method

3. The attempt at a solution
The critical points are 3 and 5. But I don't know what to do with expressions involving modulus signs.

2. Oct 26, 2012

### SammyS

Staff Emeritus
For what values of x is |x|-3 = 0 ?

For what values of x is |x|+1 = 0 ?

3. Oct 26, 2012

### haruspex

Not sure how you're defining critical points, but interesting things will happen at -3, 1, 3 and 5. I would break it into the five ranges those points generate and consider each separately.
But first, there's a very easy simplification. Think about the (|x|+1) term.

4. Oct 26, 2012